Solve 96+323=33v^2/56

$$96 + 323 = \frac { 33 v ^ { 2 } } { 56 }$$

Solve for v

$$v = \frac{2 \sqrt{193578}}{33} \approx 26.665151472$$

$$v = -\frac{2 \sqrt{193578}}{33} \approx -26.665151472$$

Steps by Finding Square Root

Multiply both sides of the equation by 56.

$$5376+18088=33v^{2}$$

Add 5376 and 18088 to get 23464.

$$23464=33v^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$33v^{2}=23464$$

Divide both sides by 33.

$$v^{2}=\frac{23464}{33}$$

Take the square root of both sides of the equation.

$$v=\frac{2\sqrt{193578}}{33} v=-\frac{2\sqrt{193578}}{33}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 56.

$$5376+18088=33v^{2}$$

Add 5376 and 18088 to get 23464.

$$23464=33v^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$33v^{2}=23464$$

Subtract 23464 from both sides.

$$33v^{2}-23464=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 33 for a, 0 for b, and -23464 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{0±\sqrt{0^{2}-4\times 33\left(-23464\right)}}{2\times 33}$$

Square 0.

$$v=\frac{0±\sqrt{-4\times 33\left(-23464\right)}}{2\times 33}$$

Multiply -4 times 33.

$$v=\frac{0±\sqrt{-132\left(-23464\right)}}{2\times 33}$$

Multiply -132 times -23464.

$$v=\frac{0±\sqrt{3097248}}{2\times 33}$$

Take the square root of 3097248.

$$v=\frac{0±4\sqrt{193578}}{2\times 33}$$

Multiply 2 times 33.

$$v=\frac{0±4\sqrt{193578}}{66}$$

Now solve the equation v=\frac{0±4\sqrt{193578}}{66} when ± is plus.

$$v=\frac{2\sqrt{193578}}{33}$$

Now solve the equation v=\frac{0±4\sqrt{193578}}{66} when ± is minus.

$$v=-\frac{2\sqrt{193578}}{33}$$

The equation is now solved.

$$v=\frac{2\sqrt{193578}}{33} v=-\frac{2\sqrt{193578}}{33}$$